Castro, Alejandro M. (2007) Interacción fluido estructura: elementos finitos en acústica, formulación ALE y esquemas staggered / Fluid structure interaction: finite elements in acoustics, ALE formulation and staggered schemes. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En este trabajo se lleva a cabo el estudio de problemas de interacción fluido estructura básicamente sobre dos clase bien diferenciadas de problemas. Por un lado se trata la resolución de problemas en el campo de la acústica. La motivación para la incursión en dicho campo proviene del interés en el grupo de trabajo en el cual se ha desarrollado la tesis en una cavidad resonante utilizada para estudios de cavitación y sonoluminiscencia. El desafío en este problema consiste en el acople de dos modelo matemáticos bien diferentes para el fluido y la estructura. Esta última siendo que se trata de un casquete delgado, requiere la aplicación de técnicas especiales para su modelado. En esta tesis se utilizan elementos de Serindipity con interpolación cúbica para el modelado de tales estructuras. Se investiga la obtención de los modos de resonancia del sistema acoplado y los cambios producidos al agregar pérdidas de energía, siendo que en este último caso se resuelven las ecuaciones en el campo de los números complejos. En contra parte, se tratan problemas de interacción fluido estructura en donde las deformaciones del dominio no pueden ser despreciadas. Como aplicación a este tipo de problemas se trata el caso de un tubo con paredes flexibles simulando una situación similar a la encontrada en problemas hemodinámicos en donde el fluido, sangre, circula pulsatoriamente por las arterias e induce en ellas deformaciones del orden de su diámetro. Luego, este problema requiere el tratamiento de las ecuaciones de Navier-Stokes, la descripción de estas en un dominio deformable y la interacción con la estructura. Para las ecuaciones de Navier-Stokes se hace uso las formulaciones estabilizadas SPGP y GLS. La deformación del dominio con el tiempo se trata mediante el uso de descripciones Lagragiano-Eulerianas, ALE. Se estudian diferentes esquemas ALE sobre formulaciones conservativas y no-conservativas y la importancia de la condición GCL. La interacción con la estructura es considerada por medio de un esquema staggered. Este último es implementado con subiteraciones internas de modo que el esquema resultante es totalmente implícito en el tiempo. Matemáticamente se comenta la relación entre este esquema y una formulación acoplada por multiplicadores de Lagrange. Un importante resultado de este trabajo es el desarrollo de una biblioteca para la resolución de ecuaciones en derivadas parciales no-lineales por el método de elementos finitos con la cual se han resuelto todos los problemas encontrados en esta tesis.
Resumen en inglés
In this work two very different classes of problems are treated. On the one hand acoustic field problems are studied. Previous experimental work, carried out by the research group in which this thesis was developed on a resonant device used for cavitation and sonoluminiscence studies, has been the main motivation to treat this class of problems. The challenge of this problem relies in the coupling of two well different mathematical models for the fluid and the structure. Being this later a thin shell, it is required for its modeling a special treatment. In this work it is used Serindipity elements for the modeling of such structures. Normal modes for the coupled system and the changes related to energy losses are investigated. In the case with energy losses the equations are solved in the complex field. On the other hand fluid structure interaction problems where domain deformation can not be neglected are analyzed. As an application to this type of problems it is solved the fluid flow on a pipe with deformable boundaries, simulating a similar situation encountered in hemodynamics problems where the fluid being simulated, blood, flows in a pulsing way inducing significant deformations in the arteries through which it flows. In consequence it is required to be able to deal with the Navier-Stokes equations, its formulation on movable domains and the fluid-structure interactions. SPGP and GLS stabilized finite element formulations are used for the Navier-Stokes equations treatment. Arbitrary Lagragian-Eulerian descriptions, ALE, are used to account for time domain deformations. Different temporal ALE schemes on conservative and non-conservative forms are studied and the importance of the GCL condition is investigated. A staggered algorithm is used to deal with the fluid structure coupling. This is implemented with a sub iteration loop, obtaining a full implicit temporal scheme. The connection between this scheme and a Lagrange multipliers coupled formulation is discussed. As an important result of this thesis it was developed a library for the solution of non-linear partial differential equations via the finite element method with wich was solved all of the problems of this thesis.
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
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| Palabras Clave: | Fluid-structure interactions; Interacciones fluido-estructura ; Acoustics; Acústica; ALE description; Descripciones ALE; Moving domains; Dominios móviles; Staggered schemes; Acoustic problems; Aplicaciones acústicas; Hemodynamics; Hemodinámica |
| Referencias: | [1] Charbel Farhat,Philippe Geuzaine, Gregory Brown. Application of a three- field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Computers & Fluids, (32):3–29, 2003. [2] Fabio Nobile. Numerical Approximation of Fluid-Structure Interaction Problems with Application to Haemodynamics. PhD thesis, École Polytechnique Fédérale de Lausanne, 2001. [3] E. Tezduyar, Sunil Sathe, Ryan Keedy,Keith Stein. Space-Time finite element techniques for computations of fluid-structure interactions. Comput. Methods Appl. Mech. Engrg., 195:2002–2027, 2006. [4] E. Tezduyar, M. Behr, S. Mittal. A new strategy for finite element computations involving moving boundaries and interfaces-The deforming-spatialdomain/ space-time procedure: II. Computation of free-surface flows, twoliquid flows, and flows with drifting cylinders. Comput. Methods Appl. Mech. Engrg., 94:353–371, 1992. [5] Satish Balay, William D. Gropp, Lois C. McInnes, and Barry F. Smith. Petsc home page. http://www.mcs.anl.gov/petsc, 2001. [6] Satish Balay, William D. Gropp, Lois C. McInnes, and Barry F. Smith. Petsc users manual. Technical Report ANL-95/11 - Revision 2.1.5, Argonne National Laboratory, 2003. [7] Satish Balay,William D. Gropp, Lois C. McInnes, and Barry F. Smith. Efficienct management of parallelism in object oriented numerical software libraries. In E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Modern Software Tools in Scientific Computing, pages 163–202. Birkhauser Press, 1997. [8] SLEPc web page. http://www.grycap.upv.es/slepc. [9] A. Tomás V. Hernández, J. E. Roman and V. Vidal. Slepc users manual. Technical Report DSIC-II/24/02, Universidad Politécnica de Valencia, 2007. Available at http://www.grycap.upv.es/slepc. [10] Vicente Hernandez, Jose E. Roman, and Vicente Vidal. SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Transactions on Mathematical Software, 31(3):351–362, September 2005. [11] "Timoshenko and J.M. Goodier". Theory of Elasticity. Mc. Graw Hill, 1969. [12] David Rubin W. Michael Lai and Erhard Krempl. Introduction to Continuum Mechanics. Elsevier, 1993. [13] "Gerald Wempner and Demosthenes Talaslidis". Mechanics of Solids and Shells. CRC Press, 2003. [14] Thomas J.R. Hughes. The Finite Element Method. Prentice-Hall, 1994. [15] O.C. Zienkiewics and R.L. Taylor. The Finite Element Method, volume I y II. McGraw-Hill, 1991. [16] "S. Timoshenko and S. Woinowsky-Krieger". Theory of Plates and Shells. Mc. Graw Hill, 1959. [17] Werner Soedel. Vibrations of Shells and Plates. Marcel Dekker, Ink. New York, 2005. [18] Castro Alejandro Miguel. Cálculo de Modos Naturales de Vibración en Placas con Aplicación al Cálculo de las Frecuencias de Resonancia del Motor Cohete Tronador II., 2006. Tesis de grado en ingeniería. Instituto Balseiro. SC. de Bariloche. Argentina. [19] Moshe Israeli and Steven A. Orszag. Aproximation of radiation boundary conditions. J. Comput. Phys., (41):115, 1981. [20] R. Kosloff and D. Kosloff. Absorbing boundaries for wave propagation problems. J. Comput, Phys., (63):363, 1986. [21] Philip M. Morse and K. Uno Ingard. Theoretical Acoustics. Mc. Graw Hill, 1970. [22] F. Tisseur and K. Meerbergen. The quadratic eigenvalue problem. SIAM Review, 43(2):235–286, 2001. [23] F. Tisseur and K. Meerbergen. A survey of the quadratic eigenvalue problem. Technical Report Numerical analysis report No. 370, Manchester Centre for Computational Mathematics, 2000. [24] Gustavo C. Buscaglia. Elementos Finitos en Dinámica de Fluidos con Énfasis en Viscoplasticidad y Acoplamiento Termomecánico., 1989. Tesis de grado para la carrera de Ingeniería Nuclear. Instituto Balseiro. SC. de Bariloche. Argentina. [25] J. Donea, Antonio Huerta, J.-Ph. Ponthot and A. Rodríguez-Ferran. Encyclopedia of Computational Mechanics, volume 1: Fundamentals, chapter 14. John Wiley & Sons, 2004. [26] Philippe Geuzaine, Céline Grandmont, Charbel Farhat. Design and analysis of ALE schemes with provable second-order time accuracy for inviscid and viscous flow simulations. Journal of Computational Physics, (191):206–227, 2003. [27] C. Farhat, M. Lesoinne, P. LeTallec. Load and motion transfer algorithms for fluid/structure interaction problems with non-matching descrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity. Computer Methods in Applied Mechanics and Engineering, (157):95–114, 1998. [28] Hervé Guillard, Charbel Farhat. On the significance of the geometric conservation law for flow computations on moving meshes. Computer Methods in Applied Mechanics and Engineering, (190):1467–1482, 2000. [29] Charbel Farhat,Philippe Geuzaine, Céline Grandmont. The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. Journal of Computational Physics, (174):669– 694, 2001. [30] Codina R. Blasco J. A finite element formulation for the stokes problem allowing equal velocity-pressure interpolation. Comput. Methods Appl. Mech. Engrg., 143:373–391, 1997. [31] Codina R. Blasco J. Stabilized finite element method for the transient navierstokes equations based on a pressure gradient projection. Comput. Methods Appl. Mech. Engrg., 182:277–300, 2000. [32] Codina R. Blasco J. Buscaglia G. Huerta A. Implementation of a satbilized finite element formulation for the incompressible navier-stokes equations based on a pressure gradient projection. International Journal for Numerical Methods in Fluids, 37:419–444, 2001. [33] Ramon Codina Gustavo C. Buscaglia, Fernando G. Basombrío. Fourier analysis of an equal-order incompressible flow solver stabilized by pressuregradient projection. International Journal for Numerical Methods in Fluids, 34:65– 92, 2000. [34] Taylor C. Hughes T.G. Finite Element Programming of The Navier-Stokes Equations. Pineridge Press., 1981. [35] Enzo A. Dari, Mariano I. Cantero, Raúl A. Feijóo. Computational arterial flow modeling using a parallel navier-stokes solver. ECCOMAS 2000. [36] M. Lesoinne, C. Farhat. Higher-order subiteration-free staggered algorithm for nonlinear transient aeroelastic problems. AIAA Journal, 1998. [37] S. Deparis, M. Discacciati, G. Fourestey, A. Quarteroni. Fluid-structure algorithms based on Steklov-Poincaré operators. Computer Methods in Applied Mechanics and Engineering, 2006. [38] L. Formaggia, F. Nobile, A. Quarteroni. A one dimensional model for blood flow: Application to vascular prosthesis. pages 137–153, 2002. Mathematical modeling and numerical simulation in continuum mechanics. Proceedings of the international symposium. [39] IBM Data Visualization Data Explorer. User’s Guide. Version 3 Release 1 Modifi- |
| Materias: | Física Matemática Física > Mecánica de fluidos |
| Divisiones: | Energía nuclear > Ingeniería nuclear > Termohidráulica |
| Código ID: | 240 |
| Depositado Por: | Marisa G. Velazco Aldao |
| Depositado En: | 21 Dic 2010 10:35 |
| Última Modificación: | 21 Dic 2010 10:35 |
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